Question

A railway carriage of mass 10000kg moving with a speed 15/s hits a stationary carriage of same mass. after the collision the carriage get coupled and ove together. what is their common velocity after collision?

Answer 1

`7.5ms^-1`

Explanation:

So the formula for linear momentum, `rho`, is `rho=mv`.

So before the collision, the momentum of the system is `10000*15=150000kgms^-1`.

After the collision, the momentum, according to the law of conservation of momentum, remains the same. That is, `rho_1=rho_2`, or `m_1v_1=m_2v_2`

Here, `v_2=(m_1v_1)/m_2`

`m_1v_1=150000`, we know this from our prior calculations. Now, since the second carriage gets stuck to the first one, the mass of the system, `m_2`, is equal to `20000kg`

`v_2=150000/20000`

`v_2=7.5ms^-1`

Answer 2

`=7.5"m/s"`

Explanation:

Applying the Law of Conservation of Momentum, identify the given data and set-up the needed formula to determine the common velocity of the carriages after the collision.

`"Momentum before" (P_("before"))="Momentum after"(P_(after))`

`where:`

`"Momentum(P)"="mass(m)"xx"velocity(v)"`
`P=mv`

`(P_("before")):`
The masses and the velocities of the carriages before the collision

`m_1=10,000kg; v_1="15m/s"`
`m_2=10,000kg; v_2="0m/s " ( "at rest")`

`(P_(after)):`
The masses and the velocities of the carriages after the collision

`m_1=10,000kg; v_1'=?`
`m_2=10,000kg; v_2'=?`

Take note that after the collision, both carriages moved together of same direction with the moving carriage. So that, a common velocity has been identified as follows:

`v_1'=v_2'=v_c="common velocity"`

Now, set-up the equation and plug in values in both conditions: before and after the collisions as described below.

`P_("before")=P_(after)`

`m_1v_1+m_2v_2=m_1v_1'+m_2v_2'`

but:

`v_1'=v_2'=v_c`

`m_1v_1+m_2v_2=m_1v_c'+m_2v_c'`

`(10,000kg)("15m/s")+cancel((10,000kg)("0m/s"))0=(10,000kg)(v_c)+(10,000kg)(v_c)`

`150,000"kg.m/s"+0=(20,000kg)v_c`; divide both sides by 20,000kg to isolate the variable `v_c`

`v_c=(150,000cancel(kg)."m/s")/(20,000cancel(kg))`

`v_c=7.5"m/s"`